A polarization-insensitive terahertz narrow-band filter device based on a four-period superstructure surface

Abstract

This invention proposes a polarization-insensitive terahertz narrowband filter device based on a four-period metasurface, comprising: a flexible substrate layer and a resonant layer disposed on the surface of the flexible substrate layer. The resonant layer is composed of periodically arranged four-period unit cells, each including QBIC dark-mode units and bright-mode coupling units. The QBIC dark-mode units consist of four periodically arranged dark-mode resonators, at least one of which has a different size from the others. The bright-mode coupling units consist of multiple bright-mode strip resonators surrounding the four dark-mode resonators. This invention achieves high transmittance, ultra-narrow bandwidth, high quality factor, and insensitivity of the final filter response to the incident polarization state in a specific terahertz frequency band.

Description

Technical Field

[0001] This invention relates to the technical field of terahertz filtering devices, and more particularly to a terahertz narrowband filtering device. Background Technology

[0002] Terahertz waves typically refer to electromagnetic waves with wavelengths ranging from 30 to 3000 μm and frequencies ranging from 0.1 to 10 THz. Because they lie precisely in the transition region between low-frequency infrared and high-frequency millimeter waves in the electromagnetic spectrum, terahertz waves possess the dual physical characteristics of both microwaves and light waves. With unique advantages such as high communication bandwidth and strong penetration into non-polar materials, and especially because the rotational and vibrational modes of chemical bonds in biochemical molecules exhibit unique fingerprint absorption spectra in the terahertz band, terahertz technology shows enormous application potential in broadband wireless communication, high-resolution imaging radar, and non-destructive testing of materials. However, this specific frequency band also limits the direct application of traditional microwave and optoelectronic devices. Therefore, in-depth research into the interaction between electromagnetic fields and matter in the terahertz band, overcoming existing technological bottlenecks, and developing high-performance and practical functional devices are currently the core challenges in this field.

[0003] To meet the aforementioned application requirements, two-dimensional metasurfaces, as artificial layered composite structures with subwavelength thickness, offer an ideal platform. Compared to traditional three-dimensional metamaterials, metasurfaces are composed of single-layer or a few layers of micro / nano artificial structural units, which not only significantly reduces the physical thickness and electromagnetic losses of devices but also significantly improves the system's integration. By flexibly controlling the geometry, size, orientation, and arrangement of metasurface units, precise manipulation of parameters such as electromagnetic wave amplitude, phase, and polarization can be achieved, making it one of the important technological platforms for realizing terahertz functional devices.

[0004] In recent years, flexible substrate materials, represented by polyimide (PI), have provided a novel material carrier for terahertz devices due to their excellent mechanical flexibility, outstanding thermal stability, and good resistance to chemical corrosion. Compared with traditional rigid substrates (such as silicon or quartz), these flexible media can better adapt to complex curved surfaces and have potential advantages in applications such as terahertz wearable devices, conformal devices, and in-situ sensing.

[0005] Among the many physical mechanisms of metasurfaces, electromagnetically induced transparency (EIT) has attracted much attention. Traditional EIT was initially proposed in atomic physics, stemming from the transparent window phenomenon caused by quantum interference. In metasurface systems, the EIT effect is typically explained by near-field coupling between two modes with vastly different quality factors but similar resonant frequencies. One resonant mode can couple directly with the incident electromagnetic wave, thus exhibiting a wide resonant linewidth and a low Q value, and is usually called the bright mode; the other resonant mode has extremely low radiation loss and is difficult to excite directly by the incident field, and is called the dark mode. When the resonant frequencies of the bright and dark modes are similar, the resonant coupling of the two modes under the excitation of the incident field produces destructive interference, resulting in a sharp transparent window in the transmission spectrum. Based on this theory, by introducing near-field coupling between the bright and dark modes into micro / nano structures, a "quasi-electromagnetically induced transparency" effect was successfully simulated in a classical electromagnetic system. This simulation achieved a narrow-band transmission peak with a high quality factor (Q value) at room temperature, accompanied by a significant slow-light effect.

[0006] However, traditional EIT metasurfaces based on metallic materials face severe challenges in practical applications. On the one hand, the ohmic loss of metallic materials in the terahertz band increases the nonradiative dissipation of the system and limits the resonant quality factor, thus restricting the Q-value of the transparent window of traditional metallic EIT metasurfaces and failing to meet the requirements of high-sensitivity applications. To reduce losses and improve the Q-value, some research has turned to using all-dielectric metasurfaces to achieve the EIT effect, but all-dielectric devices generally lack flexibility, making it difficult to meet the engineering requirements of future terahertz devices in conformal bonding and wearable devices. On the other hand, the complex conventional bright and dark mode structures designed to align the resonant frequency result in a significant limitation for most existing EIT metasurfaces: their mode coupling conditions are extremely sensitive to the polarization state of the incident electromagnetic wave. In complex electromagnetic environments, once the polarization state shifts, the coupling relationship is disrupted, causing the transparent window to widen or even disappear completely, severely restricting the engineering applicability of the device.

[0007] Finding a novel dark mode mechanism that can significantly improve the Q-value while maintaining polarization insensitivity, while retaining the advantages of flexible metallic metasurface engineering, has become a key technological bottleneck in this field. To further improve the resonant Q-value and attempt to address the stability issue, researchers have introduced the continuous-domain bound state (BIC) theory. First proposed in quantum mechanics in 1929, BIC describes a special class of states whose energy resides in a continuous domain but cannot radiate outwards. Introducing it into the electromagnetic domain, by meticulously designing the array's geometric parameters and introducing minute symmetry breaking, the theoretically lossless BIC can be transformed into a quasi-continuous-domain bound state (Quasi-BIC) coupled to external free space, thus achieving a high degree of energy localization with an extremely narrow resonant linewidth.

[0008] However, despite the significant physical advantages of BIC metasurfaces based on metal-flexible substrate composites, they still face irreconcilable technical contradictions when it comes to practical applications in terms of electromagnetic performance. On the one hand, in order to excite the QBIC effect, it is necessary to introduce microscale geometric symmetry breaking inside the array, as in the reference [

[22] . Huang S, Wan M, Sun M, et al. An asymmetric gaas nanocylinder quasi-bic metasurface for dual narrowband high-q perfect absorption in the near-infrared region [J]. Physical Chemistry Chemical Physics, 2026, 28 : 10749-10757]. However, this often disrupts the macroscopic symmetric arrangement in the device plane, making most existing high-Q metasurfaces highly susceptible to changes in the polarization state of incident electromagnetic waves and unable to adapt to complex and variable electromagnetic environments. On the other hand, not only do metal micro-nano structures have inherent strong ohmic losses in the terahertz band, but flexible substrate materials themselves also have non-negligible intrinsic dielectric absorption in the terahertz band. This harsh "double loss" environment further exacerbates the physical difficulty of simultaneously obtaining high Q values ​​and polarization-independent properties in this flexible composite system. Summary of the Invention

[0009] To address the technical challenge of simultaneously achieving high Q-value narrowband filtering and polarization insensitivity in existing technologies, this invention proposes a polarization-insensitive terahertz narrowband filter device based on a four-periodic metasurface. By introducing periodic perturbations, the structure evolves sequentially from a single-period to a double-period and then a four-period structure. Secondary folding in the Brillouin zone degenerates two orthogonal resonant modes at the Brillouin zone center Γ point, forming a BIC (Boiler Injection Cell). Subsequently, by altering the size of one of the four circular metal resonators, a local geometric asymmetry perturbation is introduced, transforming the BIC into a QBIC capable of coupling with free-space electromagnetic fields. Furthermore, metal strip resonators are placed around the four-periodic superlarge unit cell, coupling their broadband intrinsic resonances with the QBIC to form an EIT-like narrowband transmission response. This achieves high transmittance, ultra-narrow bandwidth, high quality factor, and insensitivity of the final filtering response to the incident polarization state within a specific terahertz frequency band.

[0010] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0011] A polarization-insensitive terahertz narrowband filter device based on a four-period metasurface, comprising a flexible base layer and a resonant layer arranged on the surface of the flexible base layer, wherein the resonant layer is composed of periodically arranged four-period unit cells, the four-period unit cell comprises a QBIC dark mode unit and a bright mode coupling unit, the QBIC dark mode unit is composed of four periodically arranged dark mode resonators, at least one of the four dark mode resonators has a size different from that of the other dark mode resonators, and the bright mode coupling unit is composed of a plurality of bright mode strip resonators surrounding the four dark mode resonators.

[0012] Preferably, the resonant layer is a metal resonant layer; the QBIC dark mode unit is composed of four dark mode metal resonators arranged two-dimensionally and periodically along the x and y directions, at least one of the four dark mode metal resonators has a size different from that of the other dark mode metal resonators; the bright mode coupling unit is composed of a plurality of bright mode metal strip resonators surrounding the four dark mode metal resonators.

[0013] Preferably, the flexible base layer adopts a polyimide PI flexible film; the metal resonant layer is a metallic copper resonant layer.

[0014] Preferably, the four dark mode metal resonators respectively correspond to four single-period units, and the four dark mode metal resonators are translated by the same distance L from the geometric center of their corresponding original single-period units toward the geometric center of the four-period unit cell, so as to realize secondary folding of the Brillouin zone and form a two-dimensionally distributed QBIC dark mode unit.

[0015] Preferably, the four dark mode metal resonators are all metallic circular resonators, three of the metallic circular resonators have the same reference radius R0, and the radius of the remaining one metallic circular resonator is R1, and R1<R0, so as to form a local geometric asymmetric perturbation inside the four-period unit cell, and obtain a quasi-bound state in the continuum capable of coupling with the free-space electromagnetic field.

[0016] Preferably, the bright mode coupling unit is composed of eight bright mode metal strip resonators surrounding the four dark mode metal resonators, the eight bright mode metal strip resonators are distributed on four boundaries of the four-period unit cell, two bright mode metal strip resonators are arranged on each boundary, the two bright mode metal strip resonators on the same boundary are symmetric about the central axis of the four-period unit cell, and the length directions of the two bright mode metal strip resonators on the same boundary are both parallel to the corresponding boundary.

[0017] Preferably, the thickness of the polyimide PI flexible film is ; the thickness of the metallic copper resonant layer is .

[0018] Preferably, the reference radius of the three metallic circular resonators is , the radius of the remaining one metallic circular resonator is The symmetrical translation distance towards the geometric center of the four-period unit cell is... .

[0019] Preferably, the width of the metal strip resonator ,length The distance between the inner endpoints of the central axis of the adjacent four-period unit cell of the metal bar resonator is... The center-to-center spacing of the metal strip resonators on the relative boundaries is N = 300 μm.

[0020] Preferably, the radius of the remaining circular metal resonator is ;

[0021] Metal strip resonator width ,length .

[0022] The beneficial effects of this invention are as follows:

[0023] High-Q QBIC resonant modes are constructed based on Brillouin zone double folding. This invention introduces periodic perturbations to evolve the metasurface structure from a single-period structure to a double-period structure and then to a four-period structure. Double folding of the Brillouin zone degenerates two orthogonal resonant modes at the Γ point, thus forming a BIC. Furthermore, by changing the radius of one of the four circular metal resonators, a local geometric asymmetry perturbation is introduced, transforming the BIC into a QBIC capable of coupling with free space. This structure achieves a narrow linewidth and high quality factor resonant response while maintaining low radiation loss.

[0024] Narrowband EIT-like transmission response is achieved through bright-dark mode coupling. This invention places metal strip resonators around the perimeter of a four-period superlarge unit cell, using their broadband intrinsic resonance as the bright mode and a QBIC formed by a circular metal resonator as the narrowband dark mode. By adjusting the structural parameters of the metal strip resonators, the resonant frequencies of the bright and dark modes are matched, generating near-field coupling. This results in an electromagnetically induced transparency-like response with high transmittance, narrow bandwidth, and high quality factor in the terahertz band, achieving narrowband filtering.

[0025] It exhibits good polarization robustness. This invention utilizes mutually orthogonal degenerate resonant modes formed by the second folding of the Brillouin zone and excites QBIC through local geometric perturbation, enabling the device to maintain a basically consistent narrowband resonant response under different linear polarization angles and left-hand and right-hand circular polarization incident conditions. This reduces the dependence of device performance on the polarization state of the incident terahertz wave and improves its applicability in complex polarization environments.

[0026] The overall structure uses only two simple metal patterns, circles and stripes, and is compatible with standard photolithography-exfoliation micro-nano processes. It can be mass-produced on flexible polyimide substrates, taking into account both high performance and flexible conformal engineering application capabilities. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 A schematic diagram of the array structure of QBIC dark mode units introduced into the four-period metasurface of the present invention.

[0029] Figure 2 This is a schematic diagram of the period doubling process corresponding to the four-period metasurface proposed in this invention, and the Brillouin zone reduction and folding process corresponding to the period doubling process.

[0030] Figure 3 This refers to the process by which the energy bands fold as the Brillouin zone folds, and mode degenerate coupling occurs at the Γ point, corresponding to the four-period metasurface proposed in this invention.

[0031] Figure 4 This invention provides a simulation of the transmittance curve of a polarization-insensitive QBIC.

[0032] Figure 5 The present invention presents a schematic diagram of an array structure in which a four-period metasurface is provided by adding a bright-mode coupling unit to the QBIC dark-mode unit to provide inherent resonance as a bright mode.

[0033] Figure 6 The simulated transmittance curves of the device under different metal strip resonator lengths B are used to characterize the coupling adjustment process between the inherent resonance of the metal strip and the QBIC resonance.

[0034] Figure 7 The transmittance simulation curves of the device under different incident polarization states, including different linear polarization angles and left- and right-hand circular polarization incident conditions, are used to characterize the polarization insensitivity of the device. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Example 1

[0037] A polarization-insensitive terahertz narrowband filter device based on a four-period metasurface, such as Figure 1 As shown, it includes a flexible substrate layer and a resonant layer disposed on the surface of the flexible substrate layer. The resonant layer is composed of four periodically arranged unit cells. The four periodic unit cells include QBIC dark mode units and bright mode coupling units. The QBIC dark mode unit is composed of four periodically arranged dark mode resonators. At least one of the four dark mode resonators has a different size from the other dark mode resonators. The bright mode coupling unit is composed of multiple bright mode strip resonators surrounding the four dark mode resonators.

[0038] Specifically, the resonant layer is a metal resonant layer; the QBIC dark mode unit consists of four dark mode metal resonators arranged in two-dimensional periodicity along the x and y directions, and at least one of the four dark mode metal resonators has a different size from the other dark mode metal resonators; the open mode coupling unit consists of multiple open mode metal strip resonators surrounding the four dark mode metal resonators.

[0039] Specifically, the flexible substrate layer is a polyimide (PI) flexible film; the metal resonant layer is a copper resonant layer.

[0040] Specifically, the four dark-mode metal resonators correspond to four single-cycle units. The four dark-mode metal resonators are translated by the same distance L from the geometric center of their corresponding original single-cycle units to the geometric center of the four-cycle unit cell, thereby achieving a second folding of the Brillouin zone and forming a two-dimensional distributed QBIC dark-mode unit cell. The side length of the single-cycle unit before the movement is half that of the four-cycle unit cell.

[0041] It should be noted that the four metal circular resonators are translated from the geometric center of their corresponding single-period unit to the geometric center of the four-period supercell, and the translation distance of the four metal circular resonators is the same, so as to form a periodic perturbation that evolves from a single-period structure to a four-period structure.

[0042] Specifically, all four dark-mode metal resonators are metal circular resonators, three of which have the same reference radius R0, and the remaining one metal circular resonator has a radius of R1, where R1<R0, so as to form a local geometric asymmetric perturbation inside the four-period unit cell, and obtain a quasi-bound state in the continuum (QBIC) that can couple with the electromagnetic field in free space. The asymmetry parameter is defined as , which is used to characterize the degree of geometric symmetry breaking inside the four-period unit cell.

[0043] It should be noted that the four metal circular resonators are respectively translated from the geometric center of their corresponding single-period unit towards the geometric center of the four-period super unit cell, and the translation distances of the four metal circular resonators are the same, so as to form a periodic perturbation that evolves from the single-period structure to the four-period structure. Through the periodic perturbation of the metal circular resonators, the metasurface structure sequentially evolves from the single period to the double period and the four period, and the first Brillouin zone corresponding to the period evolution undergoes secondary folding, so that the relevant resonant modes originally located at the edge of the first Brillouin zone are folded to the Γ point at the center of the Brillouin zone, and two mutually orthogonal resonant modes undergo mode degeneracy at the Γ point, thereby forming a bound state in the continuum (BIC). The local geometric asymmetric perturbation is introduced through the radius difference between the metal circular resonators, so that the bound state in the continuum is transformed into a quasi-bound state in the continuum (Quasi-BIC) that can couple with the electromagnetic field in free space, which not only retains the high Q characteristic of extremely low radiation loss, but also can be excited by an external field. The metal strip resonator generates a broadband inherent resonance that can directly couple with the incident terahertz wave, forming a bright mode; the quasi-bound state in the continuum generated by the metal circular resonators forms a narrowband dark mode. By making the inherent resonant frequency of the metal strip resonator close to the resonant frequency of the quasi-bound state in the continuum, the bright mode and the dark mode are coupled, and a narrowband transmission response similar to the electromagnetically induced transparency (EIT) effect is formed in the terahertz band.

[0044] Specifically, the bright-mode coupling unit is composed of eight bright-mode metal strip resonators surrounding the four dark-mode metal resonators. The eight bright-mode metal strip resonators are distributed on four boundaries of the four-period unit cell, with two bright-mode metal strip resonators arranged on each boundary. The two bright-mode metal strip resonators on the same boundary are symmetric about the central axis of the four-period unit cell, and the length B direction of the two bright-mode metal strip resonators on the same boundary is parallel to the corresponding boundary.

[0045] It should be noted that by changing the length B of the metal strip resonator, the coupling relationship between the quasi-continuous domain bound state and the inherent resonance of the metal strip resonator is adjusted, thereby regulating the frequency matching relationship and coupling state between the bright and dark modes. By introducing local geometric asymmetry perturbation into the four-period supercell and utilizing the two mutually orthogonal degenerate resonant modes formed by the second folding of the Brillouin zone, the local symmetry breaking only acts within the cell and does not disrupt the degeneracy of the two sets of orthogonal modes. Therefore, the device can maintain a basically consistent narrowband resonant response under different linear polarization angles and under left-handed and right-handed circular polarization incident conditions, achieving a polarization-robust narrowband filtering effect. The positions of the metal strip and the circular metal resonator are positioned separately. The metal strip does not need to be aligned with the center of a specific circular resonator; they should be arranged in pairs and symmetrically around the four-period supercell.

[0046] The work process is as follows:

[0047] Terahertz waves are incident perpendicularly from free space onto the flexible metallic metasurface and first couple with the symmetrically distributed metal strip resonators around the supercell. Since the metal strips can directly respond to the incident electromagnetic field, a bright mode resonance with strong radiation capability and a broad spectral line is formed.

[0048] Subsequently, the local electromagnetic field generated by the bright mode further couples near-field with the QBIC mode, which consists of four metallic circular resonators inside the supercell. Because this QBIC mode has low sensitivity to different incident polarizations, it can participate in the coupling as a polarization-robust high-Q dark mode.

[0049] When the resonant frequencies of the outer bright mode and the inner QBIC dark mode are close, coherent coupling and interference occur between the two modes. The broadband bright mode provides the main radiation channel, while the narrowband QBIC dark mode remodulates the radiation process through near-field coupling, causing a narrowband transmission peak to appear in the original broadband transmission valley, thus forming an EIT-like transparent window.

[0050] Finally, the terahertz wave modulated by the metasurface is transmitted and output from the other side of the structure. Since the internal QBIC originates from two orthogonal degenerate modes, its resonant frequency is not sensitive to changes in incident polarization. At the same time, the outer metal strips are symmetrically arranged. Therefore, the bright-dark mode coupling relationship can still be basically maintained under different linear polarization angles and left-hand and right-hand circularly polarized incident conditions, thus obtaining a stable high-Q, narrow-band, polarization-robust EIT-like transmission response around 0.8 THz.

[0051] Example 2

[0052] A polarization-insensitive terahertz narrowband filter device based on a four-period metasurface, wherein the flexible substrate is a polyimide (PI) flexible thin film with a thickness of [missing information]. The thickness of the copper resonator layer is The period of a four-period unit cell is ;

[0053] In the QBIC dark mode unit, the reference radii of the three metal circular resonators are... The radius of the remaining circular metal resonator is The radius can range from 10 to 26 μm, and the distance of symmetrical translation towards the geometric center of the four-period unit cell is... ;

[0054] In this embodiment, the QBIC dark mode units of the four-period unit cells in the metal resonant layer are arranged in a two-dimensional periodic pattern, and the unit structure and array structure are as follows: Figure 1 As shown, its basic unit is a four-period supercell that evolves through the Brillouin zone folding mechanism; as Figure 2 As shown in (a), the lattice (i.e., each single-period unit cell) is transformed from a single-period lattice to a double-period lattice and then to a four-period lattice by introducing periodic perturbations. Figure 2 (b) As shown, a first fold in the Brillouin zone corresponding to the lattice causes GM1 to fold onto the light cone, becoming QGM1. Further second folding transforms GM2 into QGM2. QGM1 and QGM2 undergo mode degeneracy at the Γ point, coupling under ideal symmetry to construct a completely energy-localized BIC. Then, by introducing... and The difference in radius breaks the symmetry inside the unit cell at the microscale, and the symmetry breaking causes the BIC to leak and transform into QBIC.

[0055] Figure 2 (a) and Figure 2 (b) The changes in real space period and the corresponding Brillouin zone evolution are presented respectively. After the period is doubled, the mode at the original boundary of the first Brillouin zone is remapped to the center of the reduced Brillouin zone. As the structure evolves from a single period to a double period, and then further to a four-period, the two guiding modes originally located at the edge of the Brillouin zone are successively translated to the vicinity of the new Γ point.

[0056] The corresponding band changes are as follows Figure 3 As shown in the diagram, in a single-period structure, the blue curve corresponds to GM1, and the red curve corresponds to GM2. Both are bound guided modes and cannot be directly coupled to free space. When the structure evolves into a two-period structure, the first Brillouin zone fold remaps GM1 to the vicinity of the new Brillouin zone Γ point, forming a quasi-guided mode QGM1. Further, after forming a four-period supercell, the second Brillouin zone fold maps GM2 to the vicinity of the Γ point, forming QGM2. At this point, QGM1 and QGM2 are frequency degenerate at the Γ point and form a nonradiative BIC through intermodal coupling.

[0057] In this embodiment of the invention, for the QBIC dark mode cell, a plane wave is used as the incident light source in the CST MWS simulation software, incident orthogonally from the top layer of the device. Periodic boundary conditions are used in both the x and y directions, and an open boundary condition is used in the z direction. A probe is added to the bottom of the substrate to detect the transmitted signal. Figure 4 As shown, simulation results indicate that under the influence of perturbations, the structure exhibits an extremely narrow resonant transmission valley near 0.803 THz, displaying typical QBIC resonance characteristics with a quality factor (Q value) as high as 3216. Furthermore, when using linearly polarized light with polarization angles ranging from 0 to 90 degrees, and left-handed and right-handed circularly polarized light as incident sources, the obtained transmission spectra and resonant frequencies almost completely overlap. These simulation results demonstrate that the mutually orthogonal degenerate resonant modes formed by the secondary folding of the Brillouin zone, combined with the QBIC excited by local geometric perturbations, enable the structure to achieve a high Q-value resonant response while maintaining good response stability to different incident polarization states.

[0058] In open-mode coupling elements, such as Figure 5 As shown, this invention adds metal strip resonators to the four edges of a QBIC dark mode unit. Specifically, the width of the metal strip resonator... The range is 7-10μm, but the effect is best at 9μm, length The range is 78-86 μm, with the best coupling effect between bright and dark modes at 78 μm. The distance between the inner endpoints of the central axis of the adjacent fourth-period unit cell is [missing value]. The center-to-center spacing of the metal strip resonators on the relative boundaries is N = 300 μm.

[0059] In this embodiment of the invention, a four-period unit cell composed of QBIC dark-mode units and bright-mode coupling units was simulated using CSTMWS simulation software with the same boundary conditions and probe settings. In this composite structure, the inherent resonance of the peripheral metal strip resonator, due to its large radiation loss, acts as a "bright mode" that can directly couple with the incident terahertz wave. The center frequency of its inherent resonance can be controlled by adjusting the length of the metal strip. Meanwhile, the high-Q QBIC excited by the Brillouin zone folding mechanism and structural perturbation in Embodiment 1 acts as a highly localized "dark mode." To more intuitively characterize the influence of the metal strip resonator length B on the coupling process of bright and dark modes, the asymmetric parameters are fixed. Under the given conditions, a parameter scan was performed on the length B of the metal strip resonator, and the results are as follows: Figure 6As shown, under these asymmetric parameter conditions, the spectral characteristics of the bright and dark modes and their evolution with changes in structural parameters are quite obvious, which is beneficial for intuitive analysis of the coupling behavior between the two modes. With the change of B, the broadband natural resonant frequency corresponding to the metal strip resonator shifts, while the resonant frequency of the QBIC changes relatively little, causing changes in the frequency detuning and coupling state between the two modes. When the resonant frequencies of the two modes gradually approach each other, they couple significantly, forming a transmission response similar to electromagnetically induced transparency (EIT).

[0060] Based on the clarified bright and dark mode coupling mechanism, and considering the device's resonant quality factor, transmittance, and response stability under different incident polarization states, this embodiment selects asymmetric parameters. Length of metal strip resonator As the preferred structural parameters, the response characteristics of the device to different incident polarization states were further investigated under these parameters, and the results are as follows: Figure 7 As shown, simulation results demonstrate that the coupling of the bright and dark modes excites a sharp, narrow-band transmission peak within a relatively wide transmission valley. The frequency at the transmission peak is 0.8 THz, corresponding to a peak transmittance of 0.83, with a bandwidth of only 3 GHz. Calculations show that its filter quality factor reaches 228. Most importantly, similar to using only the QBIC dark-mode unit, when the incident light undergoes continuous linear polarization from 0 to 90 degrees, and when both left-handed and right-handed circularly polarized light are used as incident sources, the shape, center frequency, and transmittance of this narrow-band transmission peak almost perfectly coincide. These results indicate that after introducing an external metal strip resonator and forming bright- and dark-mode coupling, the device achieves a narrow-band filtering response while maintaining a relatively stable transmission response under different linear polarization angles and left-handed and right-handed circularly polarized incident conditions, exhibiting good polarization robustness.

[0061] Example 3

[0062] A method for fabricating a polarization-insensitive terahertz narrowband filter device based on a four-period metasurface is as follows:

[0063] First, a flexible polyimide (PI) film is smoothly attached to a standard four-inch silicon wafer. Strict control is required during the attachment process to ensure the PI film surface is flat and free of noticeable bubbles or wrinkles between it and the silicon wafer, thus guaranteeing the uniformity of the subsequent photolithography pattern.

[0064] Next, a spin coating process is performed, in which a photoresist negative is uniformly spin-coated onto the PI film surface. The spin coater speed is set to 4000 RPM, thereby obtaining a uniform photoresist layer with a thickness of approximately 3 μm on the substrate surface.

[0065] Subsequently, the homogenized sample was fed into a SUSS MA6 lithography machine, precisely aligned according to the pre-designed metasurface mask pattern, and subjected to 1.5 seconds of ultraviolet exposure. The mask pre-defined a four-period ultra-large unit cell array with a period P = 320 μm, and formed corresponding circular and strip resonator patterns according to structural parameters such as R0, R1, A, B, L, M, and N, thereby transferring the designed metasurface structure into the photoresist layer.

[0066] After exposure, the sample was placed on a heating stage for inverted baking at 110 °C for 2 minutes to promote cross-linking and curing of the photoresist in the exposed area. After baking, the sample was immersed in a 2.38% TMAH solution for development for 60 seconds. After development, it was quickly rinsed thoroughly with deionized water, and the quality of the developed circular and strip-shaped microstructures was inspected under a microscope.

[0067] After confirming that the developed pattern meets the design requirements, the sample is placed in the ULVAC EI5z electron beam evaporation coating machine, and a thin film of metallic copper (Cu) is evaporated and deposited on the sample surface in a vacuum environment.

[0068] After the coating is completed, a metal lift-off process is performed, in which the sample with copper film is completely immersed in acetone solution and ultrasonic cleaning is used to dissolve the bottom photoresist layer and remove excess metal, ultimately leaving a periodic copper micro-nano structure consistent with the mask design on the PI film surface.

[0069] Finally, the microstructure of the fabricated flexible metasurface device was examined. For example... Figure 6 As shown in the microscope images after processing, both circular metal structures and strip metal structures with different orientations can be formed relatively completely, and according to... The design cycle is arranged in a regular pattern, and the relative positions and overall morphology of each structural unit are in good consistency with the design layout, indicating that the above micro-nano fabrication process can effectively prepare the designed flexible PI / Cu metasurface structure.

[0070] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A polarization-insensitive terahertz narrowband filter device based on a four-period metasurface, characterized in that, comprising: a flexible base layer and a resonant layer disposed on the surface of the flexible base layer, wherein the resonant layer is composed of periodically arranged four-period unit cells, the four-period unit cell includes a QBIC dark mode unit and a bright mode coupling unit, the QBIC dark mode unit is composed of four periodically arranged dark mode resonators, at least one of the four dark mode resonators has a size different from that of the remaining dark mode resonators, and the bright mode coupling unit is composed of a plurality of bright mode strip resonators surrounding the four dark mode resonators.

2. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 1, characterized in that, The resonant layer is a metal resonant layer; the QBIC dark mode unit is composed of four dark mode metal resonators arranged two-dimensionally and periodically along the x and y directions, and at least one of the four dark mode metal resonators has a size different from that of the remaining dark mode metal resonators; The bright mode coupling unit is composed of a plurality of bright mode metal strip resonators surrounding the four dark mode metal resonators.

3. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 2, characterized in that, The flexible base layer adopts a polyimide PI flexible film; the metal resonant layer is a metallic copper resonant layer.

4. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 3, characterized in that, The four dark mode metal resonators respectively correspond to four single-period units, and the four dark mode metal resonators are translated by the same distance L from the geometric center of their corresponding original single-period units toward the geometric center of the four-period unit cell, so as to realize secondary folding of the Brillouin zone and form a two-dimensionally distributed QBIC dark mode unit.

5. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 4, characterized in that, The four dark mode metal resonators are all metal circular resonators, three of the metal circular resonators have the same reference radius R0, and the radius of the remaining one metal circular resonator is R1, and R1<R0, thereby forming a local geometric asymmetric perturbation inside the four-period unit cell, and obtaining a quasi-bound state in the continuum capable of coupling with the electromagnetic field in free space.

6. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 5, characterized in that, The bright mode coupling unit is composed of eight bright mode metal strip resonators surrounding the four dark mode metal resonators, the eight bright mode metal strip resonators are distributed on four boundaries of the four-period unit cell, two bright mode metal strip resonators are arranged on each boundary, the two bright mode metal strip resonators on the same boundary are symmetrical about the central axis of the four-period unit cell, and the length directions of the two bright mode metal strip resonators on the same boundary are both parallel to the corresponding boundary.

7. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to any one of claims 3-6, characterized in that, The thickness of the polyimide (PI) flexible film is ; The thickness of the copper resonator layer is .

8. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 5 or 6, characterized in that, The reference radii of the three metal circular resonators are The radius of the remaining circular metal resonator is The symmetrical translation distance towards the geometric center of the four-period unit cell is... .

9. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 6, characterized in that, Metal strip resonator width ,length ; The spacing between the inner endpoints of the central axis of the adjacent four-period unit cell of the metal bar resonator is The center-to-center spacing of the metal strip resonators on the relative boundaries is N = 300 μm.

10. The polarization-insensitive terahertz narrowband filter device based on a four-period metasurface according to claim 7, characterized in that, The radius of the remaining circular metal resonator is ; Metal strip resonator width ,length .

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